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Certain spells in Arkham Horror can only be cast on upkeep. One example is "Voice of Ra":

Upkeep Phase: You may cast and exhaust to gain +1 to all skill checks
for the rest of this turn.

The rules state:

During the Upkeep Phase, each player takes the following actions, in
order.

Refresh Exhausted Cards

Perform Upkeep Actions

Adjust Skills

The Adjust Skills action states:

Finally, each player may adjust his investigator’s skills using the
three skill sliders he placed on his investigator sheet during game
setup. This process, as well as a general description of how skill
sliders work, is explained in the “Adjusting Skills” diagram.

Casting a spell doesn't fall into any of those categories. I suspect that these are the things you must do on your upkeep, but you can also do additional things, such as cast spells. But the use of the word "Finally" in the Adjust Skills action could mean that this must be the last thing you do during your upkeep, although I don't think that is the case.

Question:

When during your upkeep can you cast upkeep spells? Can I cast them even before the Refresh Exhausted Cards action? In the case of "Voice of Ra" this would allow me to cast it twice in once turn.

Edit

Answers so far have said that casting spells is a mandatory upkeep action. This may be the case, but I still think the rules are ambiguous about that. The rules for upkeep actions state:

After refreshing his exhausted cards, each player must review his
investigator’s cards to see if any of them have an Upkeep action. Each
player must perform all Upkeep actions listed on his investigator’s
cards every turn.

You are not required to cast Voice of Ra every turn. Therefore, Voice of Ra is not an upkeep action. This makes no distinction between optional and mandatory upkeep actions. The text of Voice of Ra however may make the casting of it optional. This too seems a little ambiguous. Even if this is the case, how are spells that are castable during "Any Phase" treated. Can they therefore not be cast during the upkeep (even though upkeep is a phase) because they don't have an upkeep action?

Also, if spells must be cast during the upkeep action, it means you will not be able to adjust your skills before casting. It seems a little strange to me that a spell you are casting this turn must be based off last turn's skills.

The thing everybody agrees on is that spells are cast after the 'Refresh Exhausted Cards' step. Whether or not you're allowed to cast spells after moving skills sliders is debateable. An interesting point that is brought up is that Upkeep spells (at least until the reprint of Curse of the Dark Pharaoh) said

Upkeep: You may cast and exhaust...

compared to other spells which said

Any Phase: Cast and exhaust to....

Which makes me believe that these cards have the following rule from the rule book apply (bolded words are my emphasis)

Perform Upkeep Actions

After refreshing his exhausted cards, each player must
review his investigator’s cards to see if any of them
have an Upkeep action. Each player must perform all
Upkeep actions listed on his investigator’s cards every
turn. Upkeep actions may be taken in any order the player wishes. Bless, Curse, Bank Loan, and Retainer cards
do not require an upkeep roll during the first Upkeep
Phase after an investigator acquires them.Each player must perform all
Upkeep actions listed on his investigator’s cards every
turn.

Since the spells have Upkeep: on them, they count as upkeep actions (much like Blessings, Curses, Retainers, and Bank Loans) and have to be used during the Perform Upkeep Actions step, but they have the may qualifier on them they don't have to cast. Fantasy Flight just got lax with the Upkeep spell verbiage in later expansions I guess.

But really, as long as you aren't casting/refreshing/recasting spells during upkeeping you're good.

EDIT:

I should clarify that I'm not really a strong proponent of the specific logic in the argument above, I was just summarizing the thread I linked to. It seems like a nice idea but causes too many issues when you find Upkeep spells that lack the word 'may'.

A similar argument is that you have to use the evade bonus from a dark cloak when making evade checks because there's nothing that says you have the option of not using items. (Example situation: If you wanted to take combat damage and get sent to the hospital without having to make a horror check). I find forcing Investigators to use items in any situation where they could be applicable to be a bit extreme. This would fall under that same category for me. Personally, when Fantasy Flight said

must perform Upkeep actions listed on his investigator's cards

I read it as

may perform any Upkeep actions listed on his investigator's item cards and must perform any Upkeep actions listed on his investigator's non-item cards

since I don't think manditory item use is reasonable. If you believe that item bonuses are non-optional, then casting spells during upkeep would be non-optional as well.

EDIT 2:

As far as the the timing of the actions go (since that was actually what the question was about) the rules say this about the Refresh step (emphasis mine):

At the start of the Upkeep Phase, each player
refreshes...

and this about the Adjust step (as you've noted) (again, emphasis mine):

Finally, each player may adjust...

This would suggest that, within the Upkeep Phase, nothing can come before the refresh step and nothing can follow the adjust skills step. Thus, spells would have to fall someplace in the middle, regardless of them being mandatory or not. You could however interpret "finally" as simply denoting the last item in a list rather than meaning "At the end of upkeep phase", but I think it's pretty clear that the Refresh step is the very first thing that happens.

If Voice of Ra has a mandatory upkeep action that lets you optionally do something, why is it written as "Upkeep Phase:" as opposed to other upkeep actions which are written as "Upkeep:" or other spells which may say "Movement:" (these dont have the word "phase" in the phase qualifier portion of the text).
–
MattOct 26 '12 at 14:16

@Matt Looking through my set of cards, Voice of Ra says 'Upkeep' rather than 'Upkeep Phase'. Perhaps that specific wording is from the initial printing, or maybe it's a typo on the AH wiki.
–
EvilAmarant7xOct 26 '12 at 14:42

Ill assume its a typo on the wiki until I can check my cards
–
MattOct 26 '12 at 14:55

I don't have The Curse of the Dark Pharaoh (Revised Edition) where the rules could be different, and the AH wiki could not have the exact text, but "Denying the Ancient One" appears to be an upkeep spell that doesn't say "You may cast..." arkhamhorrorwiki.com/Denying_the_Ancient_One_%28Revised%29 so I might not agree with the required upkeep action that lets you optionally cast the spell answer.
–
MattOct 26 '12 at 15:03

From the revised CotDP expansion, Denying the Ancient One, Revelation of Script, and Shroud of Shadow say Upkeep: Cast and exhaust. Feeding the Mind says Upkeep: You may cast and exhaust. Not sure what you want to take from that. Fantasy Flight has acknowledged miswordings in other instances in this game, I wouldn't take these cards as exceptions to the rest of the Upkeep spells.
–
EvilAmarant7xOct 26 '12 at 15:07

I think it takes a lot of devious rules lawyering to think of casting spells during upkeep as anything other than (optional) "upkeep actions".

If you are really adamant on arguing that they are something substantially different from the other (compulsory) upkeep actions that definitely must happen between refreshing the cards and moving the silders, I think it's difficult to definitively prove to you that spells shouldn't be cast at weird moments during upkeep, enabling strange effects like, as you say, casting spells twice in one turn.

However, the commonsense reading of upkeep, IMO, is that refreshing happens, then most other things (including upkeep spellcasting), then skill adjustment. Any other interpretation just seems a bit like trying too hard.

Spells would definitely be classified as "upkeep actions" and would happen in the second step of upkeep that you outlined. You would not be able to cast spells before refreshing exhausted cards (it would be broken, as you suggest). You are free, of course, to cast the spells in whatever order is most effective.